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Arithmetic Teaching Apparatus

Tests

Throughout most of the nineteenth century, teachers tested the progress of students with oral examinations, often held at the blackboard. By the end of the century, more formal written examinations were used in some states to test graduates of academies in high schools and to accredit teachers. A few universities began to offer advanced degrees in education, and faculty there reflected on the history of mathematics education in this country.

At the same time, as the number of students attending school expanded, as high schools began to offer vocational training, and as manufacturing became more efficient, several authors worried about maximizing the efficiency of schools. A variety of standardized examinations were introduced to predict the performance of students, to point up areas where they needed work, and to evaluate school systems.

This collection of tests for students in grades six, seven and eight is an early example of a paper and pencil standardized examination for school children. Included (printed to be read going one direction) are seven tests collectively designed to measure general intelligence. They include multiple choice tests of analogies, arithmetic word problems, vocabulary, matching symbols to numerals (called substitution), verbal ingenuity, arithmetical ingenuity, and synonyms and antonyms. A test of silent reading ability and seven tests of operations of arithmetic are printed to be read going in the other direction.

These tests were developed at the Bureau of Educational Research at the University of Illinois by Walter S. Monroe and B. R. Buckingham. They were published by The Public School Publishing Company of Bloomington, Illinois, and also are known as the Illinois Examination. This version is copyrighted 1920.

This example of the test is from the collection of clinical psychologist David Shakow.

This paper and pencil arithmetic examination was part of the first (1922) edition of a set of tests developed at Stanford University by professor of psychology Lewis M. Terman, statistician and assistant professor of education Truman L. Kelley, and doctoral student Giles M. Ruch (Stanford PhD., 1922). World Book Company published the tests. Scores on the arithmetic examination are divided into two parts: computation of numerical examples, and word problems.

The Stanford Achievement Tests were designed to test the accomplishments of school children in grades two through eight. Editions of the examinations are still in print.

This example of the test is from the collection of clinical psychologist David Shakow.

Reference:

Stanford University, Annual Report of the President of Stanford University, Stanford University: By the University, 1922, pp. 186, 281.

Just before World War I, Stuart A. Courtis, a teacher at a private school for girls in Detroit, Michigan, developed the first widely available standardized tests of arithmetic. His goal was to measure the efficiency of entire schools, not the intellectual ability of a few students.

Courtis went on to become supervisor of educational research in the Detroit public schools. There he developed a set of lesson cards in arithmetic for students in the third through eighth grades. The tests were originally published under his name by World Book Company.

This is a teacher’s manual for a later edition of the drill cards. Courtis’s name does not appear. Courtis withdrew his arithmetic tests from the market in 1938 because he had come to doubt their validity.

The manual was the property of Brooklyn school teacher L. Leland Locke.

By the 1920s, mathematics educators increasingly turned to standardized tests as a way to measure what students knew, to predict what they could learn, and to determine where they had difficulties. This test had sections on addition, subtraction, multiplication, and division. The final two sections were on fractions, decimals, and percentages; and on a combination of problems. The authors were Raleigh Schorling (1887–1950), John R. Clark (1887–1986), and Mary A. Potter (1889–1993?). World Book Company published the four page leaflet in 1928. Versions of the test would be published for decades.

By 1926, when the test was first published, Schorling and Clark had obtained their PhDs from Teacher’s College of Columbia University. After earning his doctorate, Clark headed the mathematics department of the Chicago State Teacher’s College, and then in 1920 returned to teach in the Department of Mathematics Education at Teacher’s College. He remained there until his retirement in 1952.

Schorling taught at the Lincoln School of Teacher’s College. He left in 1923 to become the first principal of the University High School at the University of Michigan, and completed his Teacher’s College doctorate in 1924. He remained at Ann Arbor for the rest of his career, serving as well as a professor of education at the university. Mary Potter obtained her undergraduate degree from Lawrence College in Appleton, Wisconsin, in 1913. She taught in several Wisconsin school districts, settling in Racine by 1920 and living there the rest of her working life.

At the Lincoln School, Schorling and Clark worked to reform arithmetic education by emphasizing the affairs of daily life. Their efforts led them to author new textbooks as well as new tests. Schorling, Clark, and Potter were all active in the establishment of the National Council of Teachers of Mathematics in 1920.